Through the Ref.[1]}, in the extended phase space of the AdS spacetime, one can show that the Hawking-Page temperature and the minimum black hole one share similar dependence on the pressure, \(T\sim \sqrt{P}\)  with different \(d\) -dependent coefficients
\(T_{HP}=2\sqrt{\frac{d-2}{(d-1)\pi }\times P},\quad T_{min}=2\sqrt{\frac{d-3}{(d-2)\pi }\times P}.\) 
